Fast and Cost-Effective Online Load-Balancing in - Computing ...

KONSTANTINOU ET AL.: FAST AND COST-EFFECTIVE ONLINE LOAD-BALANCING IN DISTRIBUTED RANGE-QUERIABLE SYSTEMS 1359
Fig. 10. Completion time, exchanged messages and items and MIG to NIX ratio of NIXMIG and Item Balancing for various zipfian values.
and MIG. In addition, NIXMIG requires less than half the
messages compared to IB: IB requires a large number of
probing messages, whereas NIXMIG uses the underloaded
node location mechanism described in Section 4. Furthermore,
the number of required messages in the IB algorithm
increases more due to the fact that mostly node migrations
are performed, as its MIG to NIX ratio is near 0.5 (see the
fourth graph).
In the third graph, we notice that NIX requires two
orders of magnitude more item exchanges than MIG and
NIXMIG due to the iterative key transfer procedure. What is
more, NIXMIG requires roughly the same number of item
exchanges compared to MIG. NIXMIG outperforms IB
whereas in skewed workloads NIXMIG exchanges one
third of the items compared to IB: the cooperative nature of
NIXMIG minimizes unnecessary load movement (thus item
exchanges) back and forth, unlike IB where each node acts
on its own. We observe that the IB’s number of exchanged
messages and items drops when the workload is less
skewed: IB performs less balancing actions, as it cannot
easily locate nodes that their load differs by a fraction of ".
Finally, in the fourth graph, we present NIXMIG’s and
IB’s ratio of migrations to simple neighboring item
exchange operations for various pulse widths. Here, we
notice NIXMIG’s workload adaptivity: in extremely skewed
workloads of 3-5 percent pulse widths mostly node
migrations are used (recall from Algorithm 2 that each
migration requires two neighboring item exchanges, thus
the ratio in plain migrations is 0.5). When the pulse’s width
is increased, the ratio drops as load is absorbed using more
neighboring item exchanges and costly remote migrations
are avoided. On the contrary, IB most of the times carelessly
employs node migrations.
These experiments confirm NIXMIG’s adaptivity to an
arbitrary workload, as it identifies the most effective
balancing action, combining the advantages and avoiding
the disadvantages of both plain remote migrations and
plain neighboring item exchanges. We continue our experimental
analysis with a more thorough comparison of
NIXMIG against IB.
In Fig. 11, we present a system’s load snapshot after
100 seconds for the two algorithms for a 3 percent pulse. We
notice that, unlike IB (dotted line), NIXMIG (solid line) has
successfully dropped almost every node’s load under its
thres value (horizontal red line). Moreover, in Fig. 12, we
present the variation of exchanged messages during time
for the NIXMIG and the IB algorithm. We notice that
NIXMIG constantly performs less message exchanges than
IB. What is more, in the IB algorithm, we notice the constant
traffic posed by the random probing messages.
In Fig. 10, we present the performance results of NIXMIG
against IB for the zipfian setting. In this situation, the
workload’s skew increases as the parameter increases
unlike the pulse setting where the skew decreases as the
pulse width increases. In the first graph, we notice that
NIXMIG’s completion time is similar to the one in the pulse
setting. On the other hand, IB’s completion time increases
compared to the respective completion time for the pulse
setting: in the zipfian case, the load is spread more
uniformly compared to the pulse setting, making it harder
for IB to identify load imbalances. In any case, NIXMIG is
three times faster than IB. In the second graph, we notice
that NIXMIG requires a constant number of messages with
a slight drop in the less skewed workload area, as more
neighboring item exchanges are performed. On the other
hand, IB requires constantly more messages due to the
reasons mentioned in the previous paragraph. In the
workloads with >3, NIXMIG requires one sixth of
the messages that IB requires. In the third graph, we
observe that NIXMIG’s and IB’s behavior in item exchanges
is similar as in the pulse setting. NIXMIG performs more
item exchanges than IB in the less skewed workloads of
Fig. 11. Load snapshot at t ¼ 800 sec for a 3 percent pulse.
Fig. 12. Number of exchanged messages during time for a 3 percent
pulse.